# Help Needed: I'm Stuck on Steps and Not Sure If They're Correct

• MHB
• Joe20
In summary: The expression [(p.q)-(3p.r)] /(p.p) represents a scalar value, not a lambda. This method is more efficient and avoids the need for tedious computations using vector components.
Joe20
I have done up some of the steps. I got stuck and not sure how to continue. I am not sure if those steps are correct. Need help on that.

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Hi, Alexis87.

Alexis87 said:
I have done up some of the steps. I got stuck and not sure how to continue. I am not sure if those steps are correct. Need help on that.

I did not check the details of the work you posted, so I am not suggesting that anything you did there is incorrect. The intent of this post is to suggest an alternate method that avoids the need for computing tedious cross products using vector components.

Using the equality $p\times q = 3p\times r,$ take the cross product on both left hand sides with $p$; i.e.,

$p\times q = 3p\times r\qquad\Longrightarrow\qquad p\times(p\times q)=3p\times(p\times r)$

and now use the "BAC-CAB" BAC-CAB Identity -- from Wolfram MathWorld rule and some algebra to get your desired result (noting that the various dot products you obtain from the BAC-CAB rule are constants).

GJA said:
Hi, Alexis87.
I did not check the details of the work you posted, so I am not suggesting that anything you did there is incorrect. The intent of this post is to suggest an alternate method that avoids the need for computing tedious cross products using vector components.

Using the equality $p\times q = 3p\times r,$ take the cross product on both left hand sides with $p$; i.e.,

$p\times q = 3p\times r\qquad\Longrightarrow\qquad p\times(p\times q)=3p\times(p\times r)$

and now use the "BAC-CAB" BAC-CAB Identity -- from Wolfram MathWorld rule and some algebra to get your desired result (noting that the various dot products you obtain from the BAC-CAB rule are constants).

p x (p x q) = 3p x (p x r)

p(p.q) - q(p.p) = p(3p.r) - r(3p.p)

p(p.q) - p(3p.r) = q(p.p) - 3r(p.p)

p[(p.q)-(3p.r)] = (q - 3r) (p.p)

p [(p.q)-(3p.r)] /(p.p) = q-3r => Is it correct ? then [(p.q)-(3p.r)] /(p.p) will be the scalar or lamda?

That's correct.

## 1. What steps should I follow when I'm stuck on a problem?

When you are stuck on a problem, it's important to take a step back and assess the situation. First, make sure you understand the problem and what is being asked of you. Then, try to identify any patterns or relationships that may help you solve the problem. If you are still stuck, don't be afraid to ask for help from a colleague or supervisor.

## 2. How can I tell if my steps are correct?

One way to check if your steps are correct is to explain your process to someone else. If you can clearly and confidently explain your reasoning, it's a good indication that your steps are correct. You can also double-check your work by plugging in your solution to the original problem and seeing if it works.

## 3. What should I do if I'm not sure about a particular step?

If you are unsure about a particular step, you can try to break it down further or approach it from a different angle. It's also helpful to consult any available resources, such as textbooks or online tutorials, to get a better understanding of the concept. If you are still unsure, don't hesitate to ask for clarification from your instructor or a fellow scientist.

## 4. How can I avoid getting stuck on steps in the future?

To avoid getting stuck on steps in the future, it's important to practice problem-solving regularly. This will help you develop critical thinking skills and become more familiar with different types of problems and their solutions. It's also helpful to keep organized notes and resources that you can refer back to when needed.

## 5. Are there any tips or tricks for getting "unstuck" on a problem?

One helpful tip for getting "unstuck" on a problem is to take a break and come back to it with fresh eyes. Sometimes stepping away from a problem can help you see it in a new light. It's also helpful to break the problem down into smaller, more manageable parts. Another trick is to try solving a similar, simpler problem first to gain a better understanding of the concept before tackling the original problem.

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